An involutive GVW algorithm and the computation of Pommaret bases
type: Item
instance of: scholarly article
title: An involutive GVW algorithm and the computation of Pommaret bases
zbMATH Open document ID: 1505.13039
author: Amir Hashemi
author: Thomas Izgin
author: Daniel Robertz
author: Werner M. Seiler
published in: Mathematics in Computer Science
publication date: 2021-11-24T00:00:00Z
review text: Several algorithms computing Gröbner bases have been introduced after Buchberger's algorithm in 1965. Among them, \textit{S. Gao} et al. proposed an algorithm [Math. Comput. 85, No. 297, 449--465 (2016; Zbl 1331.13018)] that computes simultaneously Gröbner bases of a given ideal and of the syzygy module of the given generating set. This algorithm is often referred to as GVW algorithm. In this paper, the authors present two variants of GVW algorithm that compute involutive bases. The first one is a fully involutive GVW algorithm because it determines an involutive basis both for the given ideal and its syzygy module. The second one is a semi-involutive one, in the sense that it computes an involutive basis for the given ideal and a Gröbner basis for the syzygy module. The authors highlight benefits and issues of both variants. A prototype implementation in Maple 2019 is available, and the authors describe it in the paper giving some benchmark computations.
reviewed by: Cristina Bertone
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 7433042
zbMATH Keywords: Gröbner bases
zbMATH Keywords: module of syzygies
zbMATH Keywords: signature-based algorithms
zbMATH Keywords: GVW algorithm
zbMATH Keywords: involutive bases
zbMATH Keywords: quasi-stable position
zbMATH Keywords: linear coordinate transformations
zbMATH Keywords: Pommaret bases
describes a project that uses: Maple
describes a project that uses: SyzInv.mpl
MaRDI profile type: Publication
full work available at URL: s11786-021-00512-5
OpenAlex ID: W3156622747
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DOI: 10.1007/S11786-021-00512-5
description: scientific article; zbMATH DE number 7433042